Question

How do you divide `(x^2+2x+6) / (x+3)`?

Answer 1

Either by polynomial long division or synthetic division:
`color(white)("XXX")(x^2+2x+6)/(x+3) = (x-1)` with remainder `9`

Explanation:

Polynomial long division

#{: ( , , x, -1, ), ( , ,"-----","-----","-----"), (x+3, ")", x^2, +2x, +6 ), ( , , x^2, +3x, ), ( , ,"-----","-----", ), ( , , , -x, +6), ( , , , -x, -3), ( , , ,"-----","-----"), ( , , , , 9) :}#

Synthetic division

#{: (,,x^2,x^1,x^0), (,"|",1,+2,+6), ( + ,"|", ,-3,+3), (,,"-----","-----","-----"), (xx(-3),"|", 1, -1,9), ("------------",,"-----","-----","-----"), ( , ,x^1,x^0,R) :}#